Robust Data-Driven Receding-Horizon Control for LQR with Input Constraints
Jian Zheng, Mario Sznaier
TL;DR
The paper addresses robust data-driven receding-horizon control for discrete-time LQR with input constraints under $\ell_\infty$-bounded disturbance. It introduces an SDP/SOS-based framework that extends model-based LQR to the data-driven setting by explicitly handling input constraints via a tunable scaling parameter $\tau$ and updating a consistency set with all available data to tighten worst-case performance. A duality-driven reformulation reduces computational burden, enabling tractable SDP relaxations for the data-driven RH-LQR, and a polynomial SOS relaxation via Putinar's theorem yields practical solvability. Experimental results demonstrate constraint enforcement and performance improvements as more data are incorporated, with a clear path to further enhancements in multi-input scenarios and state-constrained extensions.
Abstract
This letter presents a robust data-driven receding-horizon control framework for the discrete time linear quadratic regulator (LQR) with input constraints. Unlike existing data-driven approaches that design a controller from initial data and apply it unchanged throughout the trajectory, our method exploits all available execution data in a receding-horizon manner, thereby capturing additional information about the unknown system and enabling less conservative performance. Prior data-driven LQR and model predictive control methods largely rely on Willem's fundamental lemma, which requires noise-free data, or use regularization to address disturbances, offering only practical stability guarantees. In contrast, the proposed approach extends semidefinite program formulations for the data-driven LQR to incorporate input constraints and leverages duality to provide formal robust stability guarantees. Simulation results demonstrate the effectiveness of the method.